Abstract
Size-based routing policies are known to perform well when the variance of the distribution of the job size is very high. We consider two size-based policies in this paper: Task Assignment with Guessing Size (TAGS) and Size Interval Task Assignment (SITA). The latter assumes that the size of jobs is known, whereas the former does not. Recently, it has been shown by our previous work that when the ratio of the largest to shortest job tends to infinity and the system load is fixed and low, the average waiting time of SITA is, at most, two times less than that of TAGS. In this article, we first analyze the ratio between the mean waiting time of TAGS and the mean waiting time of SITA in a non-asymptotic regime, and we show that for two servers, and when the job size distribution is Bounded Pareto with parameter , this ratio is unbounded from above. We then consider a system with an arbitrary number of servers and we compare the mean waiting time of TAGS with that of Size Interval Task Assignment with Equal load (SITA-E), which is a SITA policy where the load of all the servers are equal. We show that in the light traffic regime, the performance ratio under consideration is unbounded from above when (i) the job size distribution is Bounded Pareto with parameter and an arbitrary number of servers as well as (ii) for Bounded Pareto distributed job sizes with and the number of servers tends to infinity. Finally, we use the result of our previous work to show how to design decentralized systems with quality of service constraints.
Highlights
We explore the performance of a system composed of parallel servers in which the job size distribution satisfies the heavy-tailed property
An important result comparing the performance of these two policies [2] states that in the asymptotic regime, where the ratio of the largest to shortest job tends to infinity and the system load is fixed and low, the average waiting time of Size Interval Task Assignment (SITA) with optimal intervals is, at most, two times that of Task Assignment with Guessing Size (TAGS)
SITA and TAGS are size-based routing policies, i.e., they both use cut-offs to determine how jobs are executed in the servers
Summary
We explore the performance of a system composed of parallel servers in which the job size distribution satisfies the heavy-tailed property. If we model the servers of data centers as First-Come-First-Served (FCFS) queues, the presence of very long jobs might cause a substantial performance degradation as many short jobs must wait behind a large job for a long time. This problem is solved by using size-based routing policies, in which job sizes are divided into intervals. The second size-based routing policy is called Task Assignment with
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